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$L^p$-BOUNDEDNESS OF THE BEREZIN TRANSFORM ON GENERALISED HARTOGS TRIANGLES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 04 October 2024, pp. 1-11
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We study the
$L^p$-boundedness of the Berezin transform on the generalised Hartogs triangles which are defined by 
$$ \begin{align*}H_k:=\{(z, w)\in\mathbb C^n\times\mathbb C: |z_1|^2+\cdots+|z_n|^2<|w|^{2k}<1\},\end{align*} $$where
$z=(z_1, \ldots , z_n)$ and 
$k\in \mathbb N$. We prove that the Berezin transform is bounded on 
$L^p(H_k)$ if and only if 
$p>nk+1$.
